There are times when it may be desirable to communicate data from a transmitter to a receiver such that it is difficult or impossible for a third party to either intercept (receive and decode) or even detect that transmission. This is an area that has been worked on for several decades, in areas of modulation, detection, and interception.
One of the first approaches to clandestine communication was spread-spectrum transmission. Historically, two different approaches were used: code spreading (now widely used as code division multiple access—CDMA) and frequency hopping (FH). CDMA methods operate at relatively low power spectral density, while frequency hopping methods operate at narrow and high short-term power spectral density.
The narrow-and-high short-term power spectral densities for FH may make detection relatively easy, but the random hops over wide spacing make interception difficult.
The low power spectral density of CDMA may make these signals difficult to detect. GPS, for instance, typically operates at power spectral densities that are 10 to 20 dB below the noise floor. Describing how these signals work helps understand how this is possible and also can explain interception and detection means.
Modern modulators and demodulators work in what is called baseband methods. The original signal (RF or acoustic) is mixed down to DC using a quadrature heterodyne. In the receiver path, this technique multiplies the signal by cosine and sine of the center frequency of the signal. This may be an analog modulation or may be digital after high-speed A/D converter. The in-phase and quadrature components (corresponding to the cosine multiplication sine multiplication outputs) are combined to form complex numbers by multiplying the quadrature component by i, the square root of −1. The result is low-pass filtered, and typically decimated. On the transmit or sender side, the complex numbers are multiplied by the cosine and sine of the center frequencies, treated as if a complex number, and the real component selected. This is then output.
All modulation and demodulation operations are performed in the baseband complex signal. In a typical CDMA approach, a pseudo-noise (PN) sequence of +/−1 is selected. These sequences are usually selected from special polynomial-generated sequences that have desirable statistical properties. They tend to have Fourier transforms with broad, nearly flat response. They also tend to be nearly orthogonal to other PN sequences used permitting simultaneous use of the channel for multiple communicators. The individual +/−1 values are called “chips” and the number of chips per second tends to define the bandwidth of the system. For most systems, the chip rate in chips/sec is very close to the bandwidth in Hz. A very typical CDMA system will desire to transmit a series of bits. The modulation method is to take a full PN sequence, multiply it by 1 if we want to send a 1 bit, and multiply it by −1 if we want to send a 0 bit. In this case, the number of bits per second is equal to the number of chips per second divided by the number of chips in the PN sequence. Another scheme can combine two bits into one single PN sequence, by multiplying the sequence by:
      ±                  1        2              ±                              -          1                2              .  GPS satellites use a length 1023 Gold code (PN sequence) at 1.023 million chips/sec, for 1 code per mSec along with multiplying the sequence by +/−1 for data bits. One could, in theory, modulate 1K bits/sec on the channel, but in practice, only 50 bits/sec are modulated on the codes.
On the demodulation or recipient side of CDMA, the baseband received signal is correlated against the PN sequence used in transmission. This has the effect of coherent signal processing gain. By looking at the phase of the result of the correlation, the original data bit can be extracted. For GPS data communication, there are 1023 chips per sequence and 20 sequences per bit giving a coherent processing gain of 10 log10 (1023*20)=43 dB. For most communication systems, 4 dB of processed SNR is desirable, which means this system could, theoretically, operate 39 dB below the noise floor (43 dB process gain−4 dB required=39 dB). Because of this extremely low SNR it may be believed that it is extremely difficult to detect these signals if there was no access to the PN sequence for coherent processing gain. Unfortunately, this is not quite true.
In modern CDMA systems, such as cell phones and satellite communications, PN sequences of +/−1 are employed because they result in very low ratios of peak to average power. This is important in most systems because they tend to be power limited and chiefly limited by peak power. Furthermore, the signal consists of repeated copies of the PN sequence with each copy multiplied by a single value representing the communication bits. These structures permit exploitation of the signal by parties that may not have the PN sequence. If one takes the baseband signal, takes the magnitude squared of each sample, then takes the Fourier transform, then one discovers very sharp spikes in the spectrum at the chip rate frequency and some of its harmonics. This readily permits detection and determination of the chip rate by any observer. If one computes the autocorrelation function of a CDMA signal, computes the magnitude squared of each sample, then takes the Fourier transform, one discovers sharp spikes at the repetition rate of the PN sequence. This readily permits detection and determination of the PN sequence length. Such determination can be used to extract the original PN sequence thus permitting an interloper to correctly demodulate the data stream even if they were not originally in possession of the original PN sequence. In an electronic warfare system, the typical operation is to detect the presence of a CDMA signal via chip rate detection and then determine PN sequence period, determine PN sequence, and demodulate the communication signal.
One method to remove exploitability has been to employ extremely long PN sequences and apply data modulation to short segments of the PN sequence. The classified GPS P(Y) codes are an example, with a chip rate of 10.23 million chips per second and a PN sequence length of one week. The long PN sequence length makes it difficult to exploit autocorrelation to determine PN sequence. However, the strong statistics of the chip rate and some weak statistics on bit rate make detection easy and exploitation possible.